I would call it SF, but not 1Q84. I like Murakami, but I think a lot of his speculative work tends more towards softish magical realism and surrealism, depending on the book, because of the way the non-realistic elements are incorporated. But you’re absolutely right about Hard Boiled Wonderland (and the title localisation makes sense but always gives me a double take too… it’s kind of fitting…) Of course, science fiction has become fairly incorporated into the mainstream and the riffs on it have changed a bit. It’s only because of who OP named I would even think to comment (and pedantry maybe hhh…)
I did like your suggestion of using awards, though, a lot. Because of it I learned they revived the Hayakawa award, which could be interesting to OP too because they had a short story prize
There’s also Nihon SF Taishou, which isn’t restricted to literature and is interesting as a sample because of that.
On topic: Inter Ice Age 4 by 安部公房 is not in my opinion the finest by that author (who didn’t only write ‘pure’ SF), but I liked it, it was seminal, and you might like it too. Just 'cause you asked for classics kind of.
I don’t know about a Heinlein or Asimov analogue. I would add to the other recommendations 小松左京, who wrote a lot of futuristic apocalyptic SF.
I think there’s gonna be a talk on the historical / social influences on Japanese scifi here in a few days. Wanted to go but can’t.